Cheers and welcome to Bike Forums.
Regarding your question: many of my "flats" have in fact been slow leaks. Tube may hold air for some time, but I need to inflate it a couple of times to get home. I've sometimes done this even though I carry a patch kit and a spare tube. If I'm just a few kms from home, I'd rather do the actual fixing at home. And all pneumatic tyres leak air gradually. If you check the tyre pressure before every ride, you don't need to carry a pump for that reason. I don't necessarily check my tyres, so I carry a pump.
Regarding everything else: good thing you've (re)discovered biking, if it gives you good vibes in your current situation. Keep at it!
--J